Group #21462167 — subgroups

Subgroups — #21462167

Order 7808.

144 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519847	C₂	1	1	yes	maximal, characteristic
2	#16840772	C₂	1	1	yes	maximal, characteristic
3	#16840687	C₂	1	2	yes	maximal, complemented
4	#16840686	C₂	1	2	yes	maximal, complemented
5	M₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	—	2	1	no	—
7	#14519856	—	2	1	no	—
8	#14519847	—	2	1	no	—
9	#14519847	C₂²	1	2	yes	—
10	#14519846	—	2	1	no	—
11	#14519845	C₂²	1	1	yes	characteristic
12	#14519845	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₆₁	C₂²	1	1	yes	characteristic
14	#14519717	C₄	1	1	yes	characteristic, complemented
15	#14519716	C₂²	1	2	yes	—
16	C₁₆×D₆₁	C₄	1	2	yes	complemented
17	M₃₂×C₆₁	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
19	C₂²⋊#6923	—	4	1	no	—
20	C₂×#92420	—	4	1	no	—
21	C₄⋊#6923	—	2	1	no	—
22	C₄⋊#6923	—	2	1	no	—
23	C₄×#6923	—	4	1	no	—
24	#11758213	—	2	2	no	—
25	#11758213	—	4	1	no	—
26	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂×#92418	Q₈	1	1	yes	characteristic
28	C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
29	C₈×D₆₁	D₄	1	1	yes	characteristic
30	C₈×D₆₁	Q₈	1	1	yes	characteristic
31	C₈×D₆₁	C₂³	1	1	yes	characteristic
32	C₁₆×C₆₁	C₂×C₄	1	2	yes	—
33	#11758185	C₂×C₄	1	2	yes	—
34	C₂²×D₆₁	SD₁₆	1	1	yes	characteristic
35	C₂×#6923	—	4	1	no	—
36	C₂×#6923	—	4	1	no	—
37	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
39	C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
41	C₄×D₆₁	SD₁₆	1	1	yes	characteristic
42	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
43	#92420	—	4	2	no	—
44	C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
45	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
46	#92418	C₄⋊C₄	1	1	yes	characteristic
47	#92418	C₂×Q₈	1	1	yes	characteristic
48	C₂²×C₆₁	#106	1	1	yes	characteristic
49	C₂×D₆₁	—	4	1	no	—
50	C₂×D₆₁	#106	1	1	yes	characteristic
51	C₂×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
52	#6923	—	8	1	no	—
53	#6923	—	8	1	no	—
54	C₄×C₆₁	#106	1	1	yes	characteristic
55	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
56	Dic₆₁	#106	1	1	yes	characteristic
57	Dic₆₁	C₂×SD₁₆	1	1	yes	characteristic
58	#2155	—	61	1	no	maximal, Sylow
59	C₂×C₆₁	—	2	1	no	—
60	C₂×C₆₁	C₂×#106	1	1	yes	characteristic
61	D₆₁	—	2	1	no	—
62	D₆₁	—	2	1	no	—
63	C₂×M₃₂	—	61	1	no	—
64	C₂×#108	—	61	1	no	—
65	#427	—	61	1	no	—
66	#365	—	61	2	no	—
67	#365	—	61	2	no	—
68	C₆₁	#2155	1	1	yes	characteristic, complemented, Sylow
69	C₂×M₁₆	—	122	1	no	—
70	C₂²×C₈	—	61	1	no	—
71	#117	—	122	1	no	—
72	M₃₂	—	61	1	no	—
73	M₃₂	—	61	2	no	—
74	M₃₂	#6923	1	1	yes	characteristic, complemented
75	C₂×C₁₆	—	61	2	no	—
76	#108	—	61	2	no	—
77	#108	—	122	1	no	—
78	#107	—	122	1	no	—
79	#106	—	61	1	no	—
80	#106	—	61	1	no	—
81	C₂²×C₄	—	61	1	no	—
82	M₁₆	—	122	2	no	—
83	M₁₆	—	244	1	no	—
84	C₂×C₈	—	61	1	no	—
85	C₂×C₈	—	61	1	no	—
86	C₂×C₈	—	61	1	no	—
87	C₂×C₈	—	61	1	no	—
88	C₂×C₈	—	61	1	no	—
89	C₂×C₈	—	244	1	no	—
90	C₂×C₈	C₂×#6923	1	1	yes	characteristic
91	C₄⋊C₄	—	122	1	no	—
92	C₄⋊C₄	—	122	1	no	—
93	C₂²⋊C₄	—	244	1	no	—
94	C₄²	—	244	1	no	—
95	C₁₆	—	61	2	no	—
96	C₁₆	C₂×#6923	1	2	yes	—
97	C₂³	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	61	1	no	—
102	C₂×C₄	—	61	1	no	—
103	C₂×C₄	—	244	1	no	—
104	C₂×C₄	—	244	1	no	—
105	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
106	C₈	—	61	1	no	—
107	C₈	—	61	1	no	—
108	C₈	—	244	2	no	—
109	C₈	C₄⋊#6923	1	1	yes	characteristic
110	C₈	C₂²×#6923	1	1	yes	characteristic
111	C₂²	—	61	1	no	—
112	C₂²	—	61	1	no	—
113	C₂²	—	244	1	no	—
114	C₂²	#14519845	1	1	yes	characteristic
115	C₄	—	61	1	no	—
116	C₄	—	61	1	no	—
117	C₄	—	488	1	no	—
118	C₄	—	488	1	no	—
119	C₄	#14519845	1	1	yes	characteristic
120	C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	122	1	no	—
123	C₂	—	122	1	no	—
124	C₂	C₂×#14519845	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14519847

C₂

yes

maximal, characteristic

#16840772

C₂

yes

maximal, characteristic

#16840687

C₂

yes

maximal, complemented

#16840686

C₂

yes

maximal, complemented

M₃₂×D₆₁

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#14519846

—

#14519845

C₂²

yes

characteristic

#14519845

C₂²

yes

characteristic

C₂×C₈×D₆₁

C₂²

yes

characteristic

#14519717

C₄

yes

characteristic, complemented

#14519716

C₂²

yes

—

C₁₆×D₆₁

C₄

yes

complemented

M₃₂×C₆₁

C₄

yes

characteristic, complemented

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂²⋊#6923

—

—

—

—

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×#92418

Q₈

yes

characteristic

C₈×D₆₁

C₂×C₄

yes

characteristic

C₈×D₆₁

D₄

yes

characteristic

C₈×D₆₁

Q₈

yes

characteristic

C₈×D₆₁

C₂³

yes

characteristic

C₁₆×C₆₁

C₂×C₄

yes

—

#11758185

C₂×C₄

yes

—

C₂²×D₆₁

SD₁₆

yes

characteristic

C₂×#6923

—

C₂×#6923

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

SD₁₆

yes

characteristic

C₄×D₆₁

C₂×D₄

yes

characteristic

#92420

—

C₈×C₆₁

C₄⋊C₄

yes

characteristic

C₈×C₆₁

C₂²×C₄

yes

characteristic

#92418

C₄⋊C₄

yes

characteristic

#92418

C₂×Q₈

yes

characteristic

C₂²×C₆₁

#106

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

#106

yes

characteristic

C₂×D₆₁

C₂×SD₁₆

yes

characteristic

#6923

—

#6923

—

C₄×C₆₁

#106

yes

characteristic

C₄×C₆₁

C₂×C₄⋊C₄

yes

characteristic

Dic₆₁

#106

yes

characteristic

Dic₆₁

C₂×SD₁₆

yes

characteristic

#2155

—

maximal, Sylow

C₂×C₆₁

—

C₂×C₆₁

C₂×#106

yes

characteristic

D₆₁

—

D₆₁

—

C₂×M₃₂

—

—

—

—

—

C₆₁

#2155

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

122

—

C₂²×C₈

—

#117

—

122

—

M₃₂

—

M₃₂

—

M₃₂

#6923

yes

characteristic, complemented

C₂×C₁₆

—

#108

—

#108

—

122

—

#107

—

122

—

#106

—

#106

—

C₂²×C₄

—

M₁₆

—

122

—

M₁₆

—

244

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

244

—

C₂×C₈

C₂×#6923

yes

characteristic

C₄⋊C₄

—

122

—

C₄⋊C₄

—

122

—

C₂²⋊C₄

—

244

—

C₄²

—

244

—

C₁₆

—

C₁₆

C₂×#6923

yes

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

244

—

104

C₂×C₄

—

244

—

105

C₂×C₄

C₄⋊#6923

yes

characteristic

106

C₈

—

107

C₈

—

108

C₈

—

244

—

109

C₈

C₄⋊#6923

yes

characteristic

110

C₈

C₂²×#6923

yes

characteristic

111

C₂²

—

112

C₂²

—

113

C₂²

—

244

—

114

C₂²

#14519845

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

488

—

118

C₄

—

488

—

119

C₄

#14519845

yes

characteristic

120

C₄

C₂×C₄⋊#6923

yes

characteristic

121

C₂

—

122

C₂

—

122

—

123

C₂

—

122

—

124

C₂

C₂×#14519845

yes

characteristic

	subgroup	G/H
center	C₂	C₂×#14519845
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₈	C₂²×#6923
Fitting	M₃₂×C₆₁	C₄
socle	C₂×C₆₁	C₂×#106
hypercenter	M₃₂	#6923
hypocenter	C₆₁	#2155
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

subgroup

G/H

center

C₂

C₂×#14519845

commutator

C₈×C₆₁

C₂²×C₄

Frattini

C₈

C₂²×#6923

Fitting

M₃₂×C₆₁

C₄

C₂×C₆₁

M₃₂

C₆₁

G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

N	H ≅ G/N	type
3. #16840687	C₂	semidirect
4. #16840686	C₂	semidirect
14. #14519717	C₄	semidirect
16. C₁₆×D₆₁	C₄	semidirect
17. M₃₂×C₆₁	C₄	semidirect
68. C₆₁	#2155	semidirect
74. M₃₂	#6923	semidirect

H ≅ G/N

type

3. #16840687

C₂

semidirect

4. #16840686

C₂

semidirect

14. #14519717

C₄

semidirect

16. C₁₆×D₆₁

C₄

semidirect

17. M₃₂×C₆₁

C₄

semidirect

68. C₆₁

#2155

semidirect

74. M₃₂

#6923

semidirect

Subgroups — #21462167

Conjugacy classes of subgroups

Complements